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III. Calorimetry in Ion-Exchange Studies
THERMODYNAMICS AND POTASSIUM EXCHANGE
enthalpy change is the result of the breakage and formation of chemical bonds,
and the enthalpy of a reaction is the sum of all such events in the reactants and
products, including solvent molecules (i.e., hydration enthalpies). A negative
enthalpy change implies stronger bonds within the products and a positive enthalpy change implies stronger bonds in the reactants. The enthalpy of ion
exchange is therefore a direct measurement of binding strength and is an important quantity.
Coleman (1952) was the first to use calorimetry to measure standard enthalpies
of ion exchange (W).
He obtained enthalpies of H -Na+ and H -K exchange on a “Volclay” bentonite and an ion-exchange resin by direct measurement, and also from enthalpies of neutralization of the H+-clay or resin by
subtracting the enthalpy of neutralization of the corresponding acid and alkali.
Results for these two methods agreed to within 0.5 W/mol. Enthalpies of
Na+-K+, Ba2+-Ca2+, and Ca2+-K+ exchange were also measured and
compared with values calculated from exchange isotherm data at two temperatures using Fq. (19) in Section I1,D. Agreement was again good, always within
*lo% or k0.2 kJ/mol.
Coleman’s values were somewhat uncertain because he made no attempt to
assess the extent of exchange after the reaction, assuming that adding a large
excess of the replacing ion would give complete exchange. [That this error was
small can be inferred from the results of Maes and Cremers (1977) who obtained
exchange levels of 93-94% in Ca2 -Na+ exchange using this “excess” method.] Cruickshank and Meares (1957) overcame this problem by measuring the
enthalpy of the forward and reverse reactions of A-B exchange to a common
equilibrium point. By ensuring that the total molality at equilibrium was the same
for both experiments, and taking the algebraic difference between the enthalpies
with correction for dilution, etc. (see Section III,B), they obtained the standard
enthalpy of A-B exchange.
Meanwhile, Calvet and Pratt (1956) designed a microcalorimeter for measuring enthalpies of various physicochemical and biological reactions. Martin and
Laudelout (1963) compared three methods for determining AZf” using this type of
1. Coleman’s (1952) method of measuring the enthalpy of neutralization of an
H+-clay with an alkali, X - O H , which, after subtracting the enthalpy of
neutralization, gives A Z f O for H -X exchange
2. For exchange not involving H + , the enthalpy of complete exchange is
measured at several ionic strengths, I , and extrapolated to I = 0 where the
measured enthalpy = AZf” by definition
3. Cruickshank and Meares’ (1957) method of measuring enthalpies of A +
B and B + A exchange to a common equilibrium point and subtracting the
The results from the three methods were in reasonable agreement; those between the second and third methods differed by as much as 1.2 kJ/eq, and those
between the f m t method and the other two differed by as much as 3 kJ/eq.Many
workers have since used the third method. Laudelout et al. (1968a) measured
enthalpies of exchange for various ion pairs on Camp Berteau montmorillonite
and obtained results in good agreement (10% lower) with those calculated from
exchange isotherm data, as did Gast et al. (1969).
Calorimetry has also been used to obtain a more detailed picture of enthalpy
changes during an exchange reaction. In fact, the f m t important application of
calorimetry to ion exchange was made by Barrer et al. (1963), who showed how
enthalpy changes during ion-exchange reactions on zeolites, involving Li ,
Na+ , Cs+ , K + , Rb+ , and Ca2+, reflected different types of exchange sites.
The integral and dzyerential enthalpies obtained by Barrer et al. (explained in
Section III,B) were laboriously obtained by making many individual experiments
during several days. The third method listed was used and the enthalpies were
measured at as many as a dozen different equilibrium points. Pipetting and
injecting devices have been developed which enable enthalpies at different cation
saturations to be measured in one continuous experimental run. Harter and Kilcullen (1976) designed a pipetting device for adding and mixing exact amounts
of solution to a Calvet microcalorimeter which makes multiple reactions possible. They tested the device on reactions between clay and organic materials.
Unfortunately, in making the additions and mixes, the equipment generated
amounts of frictional heat comparable with heats measured in ion-exchange
experiments. Talibudeen et al. (1977) and Minter and Talibudeen (1982) developed an automated injection system for an LKB microcalorimeter and used it to
measure enthalpies of K+-Ca2+ exchange on soils and clays. The technique
enables a complete exchange reaction, including as many as 20 points on the
isotherm, to be measured in 2-3 days; it is sensitive enough to measure heat
changes as small as 0.1 ml. The technique is outlined in Section III,B and its
applications are described in Section IV,A-E.
The calorimetrically measured enthalpy of an ion-exchange reaction cannot be
equatedper se with the standard enthalpy of exchange, M ,as obtained directly
from exchange isotherm measurements at two or more temperatures. The measured enthalpy change represents the sum of all the enthalpy changes from (1) the
cation exchange reaction, involving the exchange of cations and the hydration of
cations and surface; (2) the solvation of the solid; (3) the dilution of the salt
solutions when mixed, and (4) the mechanical injection and mixing processes in
THERMODYNAMICS AND POTASSIUM EXCHANGE
The design of modem microcalorimeters, with two reaction cells connected
electrically in opposition, enables these enthalpy changes (2)-(4) to be compensated experimentally (Maes et al., 1976; Talibudeen et al., 1977). We are thus
left with component (l), the enthalpy of exchange, which corresponds to the
experimental conditions used and not the standard state. However, the correction
required to convert the experimental enthalpy to the standard enthalpy is merely
the enthalpy of dilution of the two salts from their final state to infinite dilution
(often referred to as the “difference in the apparent molar heat contents of the
two salts”; see Laudelout et al., 1968a; Talibudeen et al., 1977). These values
are available from tables, but at the concentrationsused are always within experimental error (Cruickshank and Meares, 1957; Barrer et al., 1963; Talibudeen et
al., 1977). That this is a reasonable assumption is confirmed by the excellent
agreement between enthalpies measured calorimetrically and those calculated
from exchange isotherms (see Laudelout et al., 1968a; Maes et al., 1976).
The standard enthalpy of exchange expresses the difference in binding strength
between one homonionic form of an exchanger and another. Although this gross
comparison is very useful, a more detailed picture of how binding strength varies
at different cation ratios would be even more useful (see Section I). For K +
exchange in particular, the first 5-1096 K + saturation is the part of the exchange
process most important to crops, because the Kf saturation of a soil seldom
exceeds 10% even after many years of treatment with K fertilizers. The measurement of enthalpies by calorimetry makes possible a detailed analysis of such
regions as well as the determination of the enthalpy of the whole reaction, as
shown by Talibudeen et al. (1977), Goulding and Talibudeen (1979, 1980), and
Talibudeen and Goulding (1983a,b).
The technique for Ca2+ --* K + exchange involves adding a small amount of
KCl solution to a suspension of a known amount of the Ca2+ form of a soil or
clay. The enthalpy of the resulting exchange of some of the Ca2+ ions for K +
ions is measured and the procedure is repeated. The extent of exchange at each
step is measured in a separate exchange isotherm experiment, and the cumulative, or integral, enthalpy change (AHx) can then be plotted against the cumulative K + saturation (x), as in Fig. 3. A detailed description of the method was
given by Talibudeen et al. (1977). The reverse reaction, K + --* Ca2+, can also
be followed to check variability and reversibility (as is also shown in Fig. 3). The
value of AHx at x = 1 is equal to the standard enthalpy of exchange within
experimental error as explained earlier.
The mxversus x curve, in almost every case, takes the form of a series of
linear segments separated by sharp changes in slope, a feature also noted for
some ion-exchange reactions in zeolites by Barrer et al. (1963). This characteristic is very significant, suggesting sharply defined groups of homogeneous exchange sites within a heterogeneous structure. To ensure that this observation is
correct, a model consisting of a series of linear segments is fitted by the least
FIG. 3. The integral enthalpy of exchange (AH,)as a function of fractional K+ saturation (x) for
K -Ca* + exchange on Upton montmofionite and Fithian ate.Some data points are omitted for
clarity. D, Ca + K 0, K -P Ca. After Godding and Talibudeen (1980).
squares approximation to the AHx versus x plot and compared with the best
smooth curve that can be fitted (Goulding and Talibudeen, 1980). In every case
the stepped straight lines give the best fit, and so there is a clear indication of
heterogeneity in the exchange process. This heterogeneity is more clearly seen
when the slope of the AHx versus x curve, the differential enthalpy of exchange
[d(AH,)ldr], is plotted against x , as in Fig. 4.Such an analysis has been used to
give new information on clay mineralogy (Section IV,C).
To complete the set of differential functions, differential free energies
[d(AGx)ldr]can be calculated from selectivity coefficients as shown by Clearfield and Kullberg (1974) with
FIG. 4. The differential enthalpy of exchange [d(M,)/dx)] as a function of fractional K+
saturation (x) for K+-Ca2+ exchange on Upton montmorilloniteand Fithian illite. After Goulding
and Talibudeen (1980).
THERMODYNAMICS AND POTASSIUM EXCHANGE
Differential entropies can then be calculated using a modified form of E q . (18):
and entropy changes during an exchange reaction can thus be analyzed.
IV. THERMODYNAMICS APPLIED TO POTASSIUM
EXCHANGE IN SOILS AND CLAY MINERALS
Ion exchange was first studied systematically by Thompson (1850) and Way
(1850, 1852), who examined the adsorption of ammonia by soil and the cations
subsequently released. Such an interest in the subject from the aspect of plant
nutrition has continued, but in the early-to-middle twentieth century, naturally
occurring and synthetic zeolites, and then synthetic (organic) resinous exchangers, became the main field of study. Interest in clay minerals as cation
exchangers was renewed in the 1940s and 1950s, however, when large quantities
of radioactive wastes began to be produced. The fixing of such nuclides as
137Cs ,Y j r 2 ,'Wo2 ,and 64Zn2 in clay mineral deposits underground was
seen as a cheap and easy way of disposing of them. Therefore much research
effort was put into understanding and predicting their ion-exchange properties,
and the Gaines and Thomas (1953) method (Section II,A) was a direct result of
Thomas and co-workers in the United States (Gaines and Thomas, 1953,
1955;Faucher and Thomas, 1954; Merriam and Thomas, 1956) were responsible
for most of the early applications to clay studies. Laudelout set up a research
group in Belgium, again concerned primarily with clays (e.g., Martin and
Laudelout, 1963; Laudelout and Thomas, 1965; Cremers and Laudelout, 1966;
van Blade1 and Laudelout, 1967; Laudelout e l al., 1968a,b), and Gast and coworkers in the United States (Gast, 1968, 1969, 1972; Gast et al., 1969) concentrated on alkali metal cation selectivity. None of these groups was primarily
interested in potassium or even in soils. Hutcheon (1966) first applied the Gaines
and Thomas method specifically to potassium exchange, using montmorillonite
as a relatively simple exchanger. Tailbudeen and co-workers in Great Britain
(Deist and Talibudeen, 1967a,b; Coulter and Talibudeen, 1968; Talibudeen,
1972; Goulding and Talibudeen, 1979, 1980) used Gaines and Thomas' equations to study potassium exchange in soils and clays, and Jensen in Denmark also
investigated K exchange using thermodynamic techniques (Jensen, 1972,
1973a,b, 1975; Jensen and Babcock, 1973) but based on equations developed by
Argersinger et al. (1950) (see Section &A).
The following parameters are derived from a thermodynamic analysis of cation exchange, presented with their physical interpretation.
1. The exchange isotherm (Fig. 1) relates the equivalent fraction of the
adsorbed cation with its equivalent fraction in solution. It can be used to indicate
selectivity in an exchange process under certain conditions (see later) or to
calculate selectivity coefficients. Exchange isotherms were classified by Sposito
(1981b) into four common types, depending on their behavior at low values of
the ordinate and abscissa (Fig. 5): (a) S type, indicative of an exchangeable ion
whose relative affinity for the exchanger is not large; (b)L type, indicative of an
ion with a high relative affinity for an exchanger; (c) H type, an extreme case of
an L type; and (d)C type, a linear isotherm indicative of nonpreference. Isotherms for K+-Ca2+ exchange have been found to be S type (Hutcheon, 1966),
L type (Jensen, 1973a), and H type (Deist and Talibudeen, 1967a), depending on
temperature, concentration, and the exchanger. Isotherms can vary greatly with
ionic strength (see Sposito, 1981b), hence the need for caution when interpreting
them. However, an isotherm at one concentration can be used to calculate isotherms at any other concentration for the same cation pair, temperature, and
exchanger (Section 11,C).
2. The (corrected) selectivity coefficient (K,) expresses the selectivity of an
exchanger for a pair of cations at a certain cation ratio. It is less ambiguous than
the exchange isotherm because it is virtually independent of ionic strength (Barrer and Klinowski, 1974; Sposito, 1981b). A plot of K,, or as is more commonly
used, In K,, against fractional saturation gives a quantitative indication of selectivity changes during an exchange reaction.
FIG.5. The four classes of exchange isotherm. Sposito (1981b).